Abstract:
Let K be a field of characteristic zero with a derivation ∂ on it (for example, (C(t), ∂/∂t)) and G be a smooth commutative group scheme over it. In this talk, we study the kernel of the differential characters K(G) of the jet space of G, known as the Manin kernel of G. When G is an abelian variety, Buium showed—using the theory of universal extensions—that the Manin kernel is a D-group scheme and a finite vectorial extension of G. We extend this result to arbitrary smooth commutative group schemes, proving that the Manin kernel K(G) remains a finite vectorial extension of G. Our approach relies entirely on a detailed understanding of the structure of jet spaces and also yields a classification of the module of differential characters in terms of primitive characters, viewed as a K{∂}-module. This is joint work with Arnab Saha.
Language: English
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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